Examples for Calculating the Effective Interest
The examples are all cases in which the added expenses are on a percentage basis.
Bill received a $10,000 one-year loan at 12% nominal interest, i.e. the adjusted interest is equal to the nominal interest and the interest is paid at the end of the year.
Bill is also charged 2% credit allocation fees. In this example, the nominal interest is 12%, and the effective interest is 14% (12% + 2%). At the end of the year, Bill repays $11,400:
$10,000 in principal, $1,200 in interest, and $200 in credit allocation fees.
David received a $10,000 one-year loan at a 12% nominal interest rate. Interest is calculated on an adjusted interest rate format, and on a monthly basis. David is also charged 2% credit allocation fees. In this example:
|The nominal interest is 12%|
|The adjusted interest is 12.68%|
|The effective interest is 14.84% (the calculation method is described below)|
The effective interest is calculated in two stages, as follows:
Stage I - calculation of the actual interest. In our example, this is 14% (= 12% + 2%).
Stage II - calculation of the adjusted interest, based on the actual interest (14%).
We will perform the calculations in the table:
|Month||Price of the Basket (Prices are Not Real)||Index in Points||Monthly Price Rise||Cumulative Price Rise|
|2/2007||$260||104||4%||4% - compared with the first observation|
|3/2007||$265||106||2%||6% - compared with the first observation|
And so forth for the other months of the year.
The amount of interest due at the end of each month (column 4) is not actually paid. It is added to the principal at the beginning of the following month (column 2).
In column 3, the product of the interest rate (14%) by (1/12) is due to the fact that the calculation is for one month (out of 12 months).
Calculation of Effective Interest when the Added Expenses are also Denoted in Dollars
When expenses denoted in USD are added to a loan, it is not always simple to translate them into some percentage of the principal, and to denote the effective interest in percentages.
For this reason (again, as required by law), the lender is obligated to report to the borrower the level of adjusted interest reflected in the transaction, but not the level of effective interest. We must calculate this for ourselves.